75813 ÷ 4 = 18953 R1
Alright, let's work through the division of 75813 by 4 step by step.

Step 1:
4 goes into 7 1 times with a remainder of 3.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 4 from 7 to get 3.
Bring next digit (5) of the dividend behind the 3 and repeat the process: 35 / 4

Step 2:
4 goes into 35 8 times with a remainder of 3.
Write down 8 as next digit of of the result. 
Result so far: 18
Subtract 32 from 35 to get 3.
Bring next digit (8) of the dividend behind the 3 and repeat the process: 38 / 4

Step 3:
4 goes into 38 9 times with a remainder of 2.
Write down 9 as next digit of of the result. 
Result so far: 189
Subtract 36 from 38 to get 2.
Bring next digit (1) of the dividend behind the 2 and repeat the process: 21 / 4

Step 4:
4 goes into 21 5 times with a remainder of 1.
Write down 5 as next digit of of the result. 
Result so far: 1895
Subtract 20 from 21 to get 1.
Bring next digit (3) of the dividend behind the 1 and repeat the process: 13 / 4

Step 5:
4 goes into 13 3 times with a remainder of 1.
Write down 3 as next digit of of the result. 
Result so far: 18953
Subtract 12 from 13 to get 1.

The final result is 18953 with a remainder of 1.